xercise 11-1 Assume the weight of a bag of microwave popcorn from a certain brand varies according to a normal distribution with mean = 2.69 oz and standard deviation = 0.05 oz. Suppose Benji was skeptical about the manufacturers claim that the mean is 2.69 oz, so he took a random sample of 12 bags of the popcorn and weighed them. Their sample mean weight was 2.65 ounces. (a) Apply the Central Limit Theorem for a sample mean to draw a sketch of the sampling distribution of the sample mean weights of bags of this microwave popcorn if samples of size n = 12 were taken over and over. Note its center (measured by the mean), spread (measured by standard deviation), and shape. (b) Is it plausible to get a sample mean weight this small (2.65 ounces) even if the manufacturers claim is true? Explain, referring to the graph you sketched in (a). (c) Should Benji continue to be skeptical that the manufacturers claim is true? Explain, referring to the graph you sketched in (a). (d) What values for the sample mean weight would provide fairly strong evidence against the manufacturers claim? Explain, again referring to the sampling distribution sketched in.